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We would like to thank Qun Luo, Shan Qu, Jiang Yuan, and two anonymous reviewers for constructive suggestions that improved the manuscript greatly. Yangkang Chen appreciates Sergey Fomel for the inspiring discussions about local orthogonalization. The paper is reproducible within the Madagascar open-source platform Fomel et al. (2013). We are grateful to developers of the Madagascar software package for providing corresponding codes for testing the algorithms and preparing the figures. This work is partially supported by the Natural Science Fund of China (grant nos.:91330108, 41374121, and 61327013), the fundamental Research Funds for the Central Universities (grant no.: HIT.BRETIV.201314), the Program for New Century Excellent Talents in University (grant no.: NCET-11-0804), the China Postdoctoral Science Foundation (grant no.: 2014M561053), the Natural Science Foundation of Hebei Province (grant no.: F2013202254), and the Texas Consortium for Computational Seismology (TCCS).